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test_fe_engine_gauss_integration.cc
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Tue, May 14, 19:08

test_fe_engine_gauss_integration.cc
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/**
* @file test_fe_engine_precomputation.cc
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Mon Jun 14 2010
* @date last modification: Mon Jul 13 2015
*
* @brief test integration on elements, this test consider that mesh is a cube
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014, 2015 EPFL (Ecole Polytechnique Fédérale de
* Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des
* Solides)
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "test_fe_engine_fixture.hh"
/* -------------------------------------------------------------------------- */
#include <gtest/gtest.h>
#include <iostream>
/* -------------------------------------------------------------------------- */
using namespace akantu;
namespace {
/* -------------------------------------------------------------------------- */
template <size_t t> using degree_t = std::integral_constant<size_t, t>;
/* -------------------------------------------------------------------------- */
template <size_t degree> class Polynomial {
public:
Polynomial() = default;
Polynomial(std::initializer_list<double> && init) {
for (auto && pair : zip(init, constants))
std::get<1>(pair) = std::get<0>(pair);
}
double operator()(double x) {
double res = 0.;
for (auto && vals : enumerate(constants)) {
double a;
int k;
std::tie(k, a) = vals;
res += a * std::pow(x, k);
}
return res;
}
Polynomial extract(size_t pdegree) {
Polynomial<degree> extract(*this);
for (size_t d = pdegree + 1; d < degree + 1; ++d)
extract.constants[d] = 0;
return extract;
}
auto integral() {
Polynomial<degree + 1> integral_;
integral_.set(0, 0.);
;
for (size_t d = 0; d < degree + 1; ++d) {
integral_.set(1 + d, get(d) / double(d + 1));
}
return integral_;
}
auto integrate(double a, double b) {
auto primitive = integral();
return (primitive(b) - primitive(a));
}
double get(int i) const { return constants[i]; }
void set(int i, double a) { constants[i] = a; }
protected:
std::array<double, degree + 1> constants;
};
template <size_t degree>
std::ostream & operator<<(std::ostream & stream, const Polynomial<degree> & p) {
for (size_t d = 0; d < degree + 1; ++d) {
if (d != 0)
stream << " + ";
stream << p.get(degree - d);
if (d != degree)
stream << "x ^ " << degree - d;
}
return stream;
}
/* -------------------------------------------------------------------------- */
using TestDegreeTypes = std::tuple<degree_t<0>, degree_t<1>, degree_t<2>, degree_t<3>, degree_t<4>, degree_t<5>>;
std::array<Polynomial<5>, 3> global_polys{
{{0.40062394, 0.13703225, 0.51731446, 0.87830084, 0.5410543, 0.71842292},
{0.41861835, 0.11080576, 0.49874043, 0.49077504, 0.85073835, 0.66259755},
{0.92620845, 0.7503478, 0.62962232, 0.31662719, 0.64069644, 0.30878135}}};
template <typename T>
class TestGaussIntegrationFixture
: public TestFEMFixture<std::tuple_element_t<0, T>> {
protected:
using parent = TestFEMFixture<std::tuple_element_t<0, T>>;
static constexpr size_t degree{std::tuple_element_t<1, T>{}};
public:
TestGaussIntegrationFixture() : integration_points_pos(0, parent::dim) {}
void SetUp() override {
parent::SetUp();
auto integration_points =
this->fem->getIntegrator().template getIntegrationPoints <
parent::type,
degree == 0 ? 1 : degree > ();
nb_integration_points = integration_points.cols();
auto shapes_size = ElementClass<parent::type>::getShapeSize();
Array<Real> shapes(0, shapes_size);
this->fem->getShapeFunctions()
.template computeShapesOnIntegrationPoints<parent::type>(
this->mesh->getNodes(), integration_points, shapes, _not_ghost);
auto vect_size = this->nb_integration_points * this->nb_element;
integration_points_pos.resize(vect_size);
this->fem->getShapeFunctions()
.template interpolateOnIntegrationPoints<parent::type>(
this->mesh->getNodes(), integration_points_pos, this->dim, shapes);
for (size_t d = 0; d < this->dim; ++d) {
polys[d] = global_polys[d].extract(degree);
}
}
void testIntegrate() {
std::stringstream sstr;
sstr << this->type << ":" << this->degree;
SCOPED_TRACE(sstr.str().c_str());
auto vect_size = this->nb_integration_points * this->nb_element;
Array<Real> polynomial(vect_size);
size_t dim = parent::dim;
for (size_t d = 0; d < dim; ++d) {
auto poly = this->polys[d];
for (auto && pair :
zip(polynomial, make_view(this->integration_points_pos, dim))) {
auto & p = std::get<0>(pair);
auto & x = std::get<1>(pair);
p = poly(x(d));
}
auto res =
this->fem->getIntegrator()
.template integrate<parent::type, (degree == 0 ? 1 : degree)>(polynomial);
auto expect = poly.integrate(this->lower(d), this->upper(d));
for (size_t o = 0; o < dim; ++o) {
if (o == d)
continue;
expect *= this->upper(d) - this->lower(d);
}
EXPECT_NEAR(expect, res, 5e-14);
}
}
protected:
UInt nb_integration_points;
std::array<Array<Real>, parent::dim> polynomial;
Array<Real> integration_points_pos;
std::array<Polynomial<5>, 3> polys;
};
template <typename T>
constexpr size_t TestGaussIntegrationFixture<T>::degree;
/* -------------------------------------------------------------------------- */
/* Tests */
/* -------------------------------------------------------------------------- */
TYPED_TEST_CASE_P(TestGaussIntegrationFixture);
TYPED_TEST_P(TestGaussIntegrationFixture, ArbitraryOrder) {
this->testIntegrate();
}
REGISTER_TYPED_TEST_CASE_P(TestGaussIntegrationFixture, ArbitraryOrder);
using TestTypes =
gtest_list_t<tuple_split_t<50, cross_product_t<TestElementTypes, TestDegreeTypes>>>;
INSTANTIATE_TYPED_TEST_CASE_P(Split1, TestGaussIntegrationFixture, TestTypes);
using TestTypesTail =
gtest_list_t<tuple_split_tail_t<50, cross_product_t<TestElementTypes, TestDegreeTypes>>>;
INSTANTIATE_TYPED_TEST_CASE_P(Split2, TestGaussIntegrationFixture, TestTypesTail);
}

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